The language used to describe the affects of certain drugs in my opinion are designed to make the medications sound better than they are. Beta blockers "prevent the release of adrenaline and noradrenaline in certain parts of the body". They highlight the heart as a "certain part" because that's what the med is prescribed for. They can also affect lungs, kidney function and blood sugar levels, so the reduced function and production of adrenaline is more widespread through the body.

As I understand it, cortisol follows the production of adrenaline - adrenaline stimulates the production of ACTH (adrenocorticotropic hormone) which is what stimulates cortisol production.
"The body releases cortisol after adrenaline, when the immediate stress has passed but the body still needs to cope."
(Cleveland Clinic)

Having adrenaline blocked in the heart and sometimes the lungs are significant places for it to be blocked. That's where natural adrenalin is used most, as well as in allergic reactions, so it would make sense that normal adrenaline production would drop with beta blockers.

I mentioned this to my doctor after starting on prednisolone, but as doctors do, she wouldn't discuss the beta blocker, or the dosage, or the possible interaction with prednisone because it was prescribed by a cardiologist years ago. From the general practitioner's bible: never tread on a specialist's toes, right or wrong. So I reduced the beta blocker gradually myself last year to half the dose, then let my doctor know. She said nothing about it but watches my blood pressure which is always still normal or slightly low. I believe the medication reduction was only possible because of a complete overhaul of my diet to low carbohydrate eating and eliminating processed food last year.
NOTE: do not reduce beta blockers yourself. Sudden reductions can be very bad for your health.

I have a new doctor for the next year, so I'll ask him for his thoughts on all this at the next appointment.